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| | Apollonius, Conics Book IV |
 | | Now, Apollonius reports that Conon of Samos treated the case where a conic section or circumference of a circle meets another conic section, but that Conon's demonstrations were incorrect. |
 | | Apollonius further reports that, in connection with Conon's flawed proofs, Nicoteles remarked that the case in which a conic section meets opposite sections could be solved, but, as Apollonius makes sure to say, neither Nicoteles nor anyone else provided a demonstration. |
 | | The existence of opposite sections may have been known before Apollonius, as the references to Conon and Nicoteles in Apollonius's prefatory letter to Book IV suggest, however, it is highly doubtful that, before the Conics, there was anywhere a more than a perfunctory treatment of them. |
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